A150692 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 0), (-1, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 26, 118, 438, 2076, 8202, 39686, 162580, 795574, 3337562, 16442636, 70151960, 347092412, 1499683362, 7441238858, 32469987622, 161429373368, 710015723282, 3534872289356, 15649665880328, 77991819382488, 347196931082462, 1731581406256604, 7744956802625172, 38648071945704428, 173572457279227396

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150689 A150690 A150691 * A150693 A150694 A150695

Adjacent sequences: A150689 A150690 A150691 * A150693 A150694 A150695

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved